Often NIEHS scientists are interested in studying the effect of a chemical on a tissue or a cell or a gene expression, etc. Accordingly, they conduct suitable dose-response or time-course experiments. Based on the available scientific knowledge, a researcher may hypothesize certain patterns of mean response with respect to dose and/or time. In some instances a researcher may also be interested in detecting the lowest dose or time point at which a significant effect is seen. Usually, the null hypothesis is a flat response and one can express the alternative hypotheses using mathematical inequalities, known as order restrictions, between the unknown parameters of interest. Order restrictions can often be expressed using a graph where each unknown parameter is denoted by a circle, and the inequality, between two unknown parameters, is denoted by an arrow that points towards the larger parameter. Order-restricted statistical inference refers to statistical procedures that take into consideration the order restrictions on the parameter space. The National Toxicology Program (NTP) routinely conducts dose-response studies to investigate the carcinogenic and toxic effects of various chemicals. Using the responses obtained at each dose, the researchers are interested in determining if tumor incidence increases with dose. As another example, in the 90-day pre-chronic toxicity studies, the NTP collects data on a wide range of variables on each animal. For each, the NTP is interested in detecting whether the dose groups have an increased (or decreased) mean response compared to the control group, but there is no prior expectation about the relationships among the doses. In this research program we are developing statistical procedures that can be useful for analyzing data, routinely generated by the researchers are NIEHS, that have the above feature. The new procedures are generally more sensitive than some of the commonly used statistical procedures. We are applying the new procedures for analyzing some of the data obtained by the researchers at NIEHS.